Teaching Quantum Theory

The recent article by Chandralekha Singh, Mario Belloni and Wolfgang Christian on Students’ understanding of Quantum Mechanics in Physics Today provoked an interesting series of letters in response. Both Robert Griffith and Travis Norsen argue that students’ understanding would be improved by replacing the usual Copenhagen/Orthodox dogma by discussion of some more recent developments in the foundations of quantum theory.

Given that I don’t actually have much experience teaching quantum theory (I have only covered a lecturer’s absence for two lectures) it is perhaps a bit presumptuous for me to contribute my thoughts on this topic. Nevertheless, I do agree wholeheartedly with the basic sentiment of both these letters. I think one can easily see that at least some of the misconceptions that Sing, Belloni and Christian have written about could be easily remedied by a bit more foundational discussion at the ground level. For example, I think the common misconception that stationary states are the only allowed states of a quantum system could be dispelled by a deeper discussion of the sense in which quantum theory is analogous to classical probability theory.

However, I think both Griffith and Norsen make a mistake in the approaches they advocate in their letters. Griffith suggests replacing the orthodoxy with his own favored approach, namely decoherent/consistent histories, and Norsen thinks we should teach students Bohmian mechanics. In fact, in his letter Griffith gives the misleading impression that his approach is universally and unproblematicallly accepted by all right-thinking physicists. Whilst the formalism certainly has quite a few adherents in quantum cosmology, it is far from true that it has received universal support from all serious thinkers on the foundations of quantum theory. Similarly, whilst I agree that Bohmian mechanics presents the clearest counterexample to many common misconceptions about quantum theory, it is far from clear that it represents the best road to future progress.

In my view, the problem is not that we are teaching the wrong orthodoxy to students, but rather that we are teaching them any orthodoxy at all, since foundations is a subject that is still mired in controversy to this day. It is hard for me to imagine any physicist who is not directly involved in foundations taking either Griffith’s or Norsen’s arguments seriously, since their letters directly contradict each other about what is the best approach to teach, and a non-specialist really has no way of deciding which one of them they should trust. The view that foundations is a murky area, with no clear reason for choosing one approach over any other is only reinforced by such arguments and it is unlikely to persuade a skeptic to change their whole teaching strategy.

On the other hand, I do believe that there are a lot of developments in foundations that have made our current understanding much clearer, and these could be usefully communicated to students. For example, we have a much clearer understanding of the “no-go” theorems, such as Bell’s theorem, and their possible loopholes, and a much clearer understanding of the space of possible realist interpretations of quantum theory. We have an improved understanding of the classical limit, via decoherence theory amongst other approaches, and quantum information theory has shown that entanglement and the understanding of quantum theory as a generalized probability theory actually have useful consequences. I believe we should teach these things as a central part of quantum mechanics courses, and not just as peripheral topics covered in the last one or two lectures, which students are instructed not to worry about because it won’t be on the final exam! We should also give students an understanding of the space of possible resolutions to foundational problems, to equip them with a BS detector for statements they are likely to hear about quantum theory. Why do I believe this? Well, simply because I think it will leave students less confused about how to understand quantum theory and because I think these areas are all increasingly fruitful avenues of research that we might want to encourage them to pursue.

The difficult question, I think, is not the why but the how. It would entail battling against the prevailing wisdom that foundations are to be de-emphasised and relegated to the end of the course. Also, good teaching materials at an appropriate level that could supplement the existing curriculum are not readily available, and that is a problem we definitely have to address if we want this to happen.

23 Comments on “Teaching Quantum Theory”

On a related note, what would your recommendations be for introductory but technical treatments of the loopholes in Bell’s Inequality (and the experiments made to test it)? I noticed a while ago that the Wikipedia article on that topic is a complete mess, worked over by people pushing all sorts of notions, probably misrepresentative in several respects, linking to arXiv preprints of unknown worth, etc. As of today, it doesn’t look like it would be useful to anybody who didn’t already know the subject. . . so what can I offer instead?

I suppose this is a special case of the general point you make in your last paragraph: teaching tools at the appropriate level just aren’t available when we need them.

That’s a good question. I know of no recent review article that covers this whole field. The most important loopholes are probably still the locality and detection efficiency loopholes, both of which are likely to be closed simultaneously in future experiments. There is an extensive literature on them, but I don’t think one can do much better than looking at some of the original papers. There’s also been more recent work on the theoretical side that has discovered and closed some other loopholes, such as the memory loophole and the coincidence time loophole. There’s certainly no review that covers these.

As one of the students, I think Joseph Emerson’s course was the ideal way to teach foundations. Dedicate an entire course to the subject. Start by teaching the parts that are not specific to any interpretation (density matrices, bell inequality, etc.) and then get a whole series of guest lecturers in to argue passionately for their own preferred interpretation. The only drawback I can see is that it would be difficult to get the same quality of guest speakers anywhere but Perimeter.

Well, of course it would be nice if every university could teach every course by inviting the top elucidators in every field to drop by and give guest lectures. It would also be very nice if every physics department suddenly decided to offer a full course on the foundations of quantum theory. This is obviously impractical, but a slightly more reasonable ideal would be to have enthusiastic lecturers at every university who are willing to spend a lot of time learning the latest developments in the subject they are teaching and figuring out a good way to communicate them to their students. Even this is too much to expect in reality, since most lecturers just don’t have that sort of time, and they cannot be expected to have unbounded enthusiasm about every aspect of the subject they are teaching.

Therefore, even if lecturers can be persuaded that foundations is interesting, it won’t have an impact on their teaching unless it is easy to incorporate the new material into their existing courses. As John Sipe pointed out to me at a recent meeting, this won’t happen on it’s own. We (i.e. me and other researchers in the field) need to write undergraduate level explanations of the main developments, designed to be easily pluggable into existing courses, and make them available on the web.

Of course, I have the same time/interest issues to deal with as the lecturers themselves, so saying that I should do it and actually doing it are two very different things.

First, I wholeheartedly agree that an intepretation-free presentation would be ideal. Second, however, I have two major concerns that came out conversations at the Denver meeting:

1. It is important that whomever were to produce such supplements or what-have-you have an up-to-date knowledge of what it means to teach a course in QM, particularly from an undergraduate standpoint. In addition it is important to recognize that many undergraduate institutions such as mine only offer a single-semester course in QM (though we are potentially adding a quantum electronics course).

2. If supplements were produced and put up on the web, how would their mere existence be publicized? Personally I don’t think it is enough to simply work your way up the Google rankings because that assumes people are going to be seeking out this material. But if we really want to change the way QM is taught, shouldn’t we be trying to get as many people as possible to do this? As such, while a textbook may have numerous flaws as a medium for dissemination, it has one major advantage even if it isn’t used and that is that traditional publishers are very good at making sure teachers know their books exist (if I get another phone call from the lady at McGraw-Hill asking if I need a textbook for anything, I’m going to pop a blood vessel in my head). Thus, even if it isn’t adopted, the publishers could (unwittingly?) be used as a medium for at least planting the seed in peoples’ heads about a foundational approach that attempts to be intepretation-independent. Then you might find more instructors doing a Google search for foundational material.

I guess, in short, I’m arguing for a more two-pronged approach based on the realities of teaching undergraduates on a daily basis.

You’re right, but web-based materials are easier to produce, don’t have deadlines, entail less of a committment on the part of the authors, and it is less of a problem if they are never completed, so I would go for that as a first attempt. Given the status of most of the perople contemplating this project, I don’t think a book is likely to get off the ground in the near future, but web supplements might have a chance. The material could later be compiled into a book if it is deemed useful, since these days many academic publishers are willing to produce paper copies of things that are already available on the web.

It should also be bourne in mind that Spekkens and Sipe are already in the process of completing a pretty comprehensive textbook on the foundations of quantum theory, so that base is already covered to a large extent. What is needed is something that can supplement a course based on one of the traditional textbooks, which most lecturers are probably not going to give up any time soon.

Matt: couldn’t agree more that an introduction to foundations would aid students’ understanding of (and thence application of) quantum theory.

Alastair Rae’s textbook (from which I first learnt quantum theory) is unusual in being a textbook which includes a decent introductory survey of interpretational issues (the latest edition even has brief mention of q info). This might then tempt students on to his fuller (but still introductory) discussions in `Quantum Physics: Illusion or Reality’ and then onwards.

At Leeds we are lucky that it is a compulsory component of the theoretical physics degree that students take the philosophy of physics course that I and my colleagues in the History and Philosophy of Science Division teach: they get an unbiased (well, relatively unbiased…) survey of foundations of both Qm and spacetime theory. Some students have gone on to do Phds in physics just because of their eye-opening from this course. In other UK universities where foundations of physics is a strength, notably Oxford, straight Physics students are free to, but not required to, take the extensive courses on foundations available.

Finally on Ian’s talk of ‘interpretation free’ above. I would want to resist trying to separate foundations results from the quetions of interpretation of the theory that often spawned them. Surely all we require is lack of dogmatism about interpretations and making sure a fair surey of views is presented to students. Practically every one of the standard options has important things to teach us about some aspect of the quantum world.

You make some good points. However, I think that the reason for stressing an “interpretation free” approach, or rather talking about the “foundations of quantum theory” rather than “interpretations of quantum theory” is to get away from the idea that this area is just “mere philosophy” and of no relevance for “physics proper” (no insult is intended – I’m just paraphrasing the standard physicist’s opinion). Every area of physics has its foundations, and in many cases more than one viable interpretation, but in most cases the subject is called foundations rather than interpretations – the latter having a bit more of a wishy-washy connotation. It is curious that this is not the case for quantum theory, and that it’s foundations are not generally thought to be a part of physics. I mean, quantum foundational research has led to novel experiments as well as to at least one whole new area of science, and if this doesn’t persuade people that foundations is relevant to physics then I honestly don’t know what would.

Although he publishes ‘physics and God’ stuff now, Paul Davies’ little book on quantum theory was quite nice, as an introduction.

I have no idea why anyone would advocate teaching QM through consistent histories (although Griffiths’ enthusiasm for it is understandable, of course).

I think that to adopt the extra complexity of a foundational/intepretational approach (and, myself, I’d maintain the distinction, but I’m not that excited about the issue either way) in teaching the subject, you’d need to show that there had really been significant advances in terms of predictive power (or at least calculation). I don’t think that it should be an issue of physics vs non-physics, although I do think that there’s an issue of science vs non-science (by which lights, there is a reasonable amount of physics that isn’t science, but that’s no big deal; the science vs non-science boundary isn’t a boundary between meaning and non-meaning, or anything like that).

Learning other interpretations or more of the foundations, however you see it, is part of the fun, in any case.

I am starting to regret the use of the word ‘free.’ What I meant (and what I think I mentioned to Matt in an e-mail), was more akin to ‘interpretation-independent’ in the sense that these foundational issues should be taught, but rather from a variety of viewpoints (without getting bogged down in such issues). Teaching all the details and nuances of the various interpretations is not necessary (and there is not enough time), but being sure that students are 1.) aware of the major ones and 2.) realize that certain ways of approaching problems stem from particular interpretations (e.g. wavefunction collapse from Copenhagen) or have multiple ways of being explained (e.g. probabilities via Everett, Bayesian, etc.). I most certainly agree that interpretational and philosophical issues should be included (Chris: your colleague Steven French was the external examiner on my PhD thesis at St. Andrews), but I think a balance must be struck both from the point of view of student learning patterns and the realities of teaching (e.g. many schools don’t even offer such courses, though, luckily, mine does and we have a heavy philosophy/theology requirement since we’re a Catholic school).

First of all, taking a foundational approach is not supposed to increase the complexity of teaching. Rather, it’s supposed to make things clearer for the students by eliminating some of the common misconceptions that students obtain from following a strict diet of Copenhagen/Orthodoxy. Admittedly, a good method of incorporating insights from foundations without losing the students and the instructor in a complicated sea of alternatives has not yet been developed, but that would be a key goal of producing foundational supplements.

Also, I think it’s fair to say that a certain portion of the students in a modern quantum physics class will go on to study at least some quantum information and computation (and I’m assuming you would call these subjects “science”). Some may even go on to specialize in the theory or experiment of this subject. A solid understanding of entanglement, Bell inequalities, and the pitfalls of using expressions like “genuinely quantum effect” are nigh on essential for a proper appreciation of this field. Some people like to forget the fact that these things were only discussed in the context of foundations for several decades and would say that I’m talking about teaching the students a little quantum information. This makes it difficult for me to argue that quantum foundations has made significant predictive advances because every time it actually does, people invent a new name for those advances so that they don’t have to be associated to the wishy-washy subject of interpretations.

As the name suggests, foundations is not necessarily about the immediate increase of predictive power, but rather it is supposed to reinforce the conceptual machinery of the theory so that predictions that were previously obscure become obvious.

I don’t think that it’s worthless to teach those issues and I certainly wouldn’t exclude entanglement and Bell inequalities (and nor was I saying that I would); I am, however, dubious that it’s the best use of teaching time, which is limited.

As for quantum information and computation, some of it’s science and perhaps some isn’t. I don’t take the position that not being science is a bad thing, however, so it’s not a big deal to me (maths mostly isn’t science, for example).

If you look at consistent histories (or, say, the decoherence functional approach of Gell-Mann and Hartle) it can be long on the potential utility of the approach in quantum cosmology, where nothing’s identifiably classical, although I’m not entirely convinced that many people get benefit in their research from it at this stage. But anyhow, I do make a distinction between foundations and intepretations; Bells’s work, Werner’s 1989 paper, etc, are, I would say, studies in foundations. Thinking about what QM means, wondering whether Many Worlds is actually true, that’s interpretations, for me. That’s just a shorthand, anyhow, but I didn’t claim that either of those was worthless, just that much of it won’t be ‘science’, based on my belief that the criterion of demarcation between science and non-science is the ability to make falsifiable predictions (which then should be followed by an attempt to falsify them).

My main point, in any case, was that I am unconvinced that teaching Consistent Histories or Bohmian mechanics is a good use of time (you don’t need either to appreciate Bell’s inequalities or entanglement, for example), although I guess that a special lecture on it would be OK (I had one, and it didn’t do me any harm, no sirree).

I think I agree with your main point, i.e. it would be a waste of time to try and develop the whole of quantum theory from the Consistent Histories or Bohmian point of view. On the other hand, there are a lot of things in the usual presentation of quantum theory that are inhereted from Copenhagen that I think are confusing and that I would try to teach in a more neutral way. A major example is the uncertainty relations, which are often described in an inaccurate way. In my undergrad courses I heard it stated several times that the uncertainty priciple should be regarded as the “starting point” for quantum theory, which gives the erroneous impression that one might actually be able to derive quantum theory from it. A more neutral and foundational approach to these issues would be worthwhile I think.

Of course, I haven’t actually had the opportunity to teach a full course in quantum theory yet, and I would have to think hard about the feasibility of incorporating these things if I did. It’s not likely to happen soon though because the quantum courses are rather popular amongst the more senior instructors round these parts.

I’m somewhat surprised that Thermodynamics is notably less popular to teach that Quantum Mechanics. I am teaching both this semester and find they compliment each other quite nicely. In fact I have thought for some time that they would make a nice two-course sequence for undergraduates at smaller institutions that only have single-semester courses in each. I have one student who is taking both and I am finding that I am constantly cross-referencing the courses when I discuss things with him.

I would say that at every educational institution I’ve attended, thermodynamics has been the least popular course (somehow weighted for general unpopularity of particular lecturers). I am not sure why; it seems to be more interesting to people that already understand it (such as the lecturer) than the people learning it, which sort of makes sense, in a way. Nevertheless, I am not entirely sure why thermo bothered so many people.

I find this post and the letters to Physics Today very interesting. I am currently a PhD student in Physics and I have taken a course in QM with Prof. Griffiths in which he taught us consistent quantum theory.

Looking back at all the QM courses I took including those in my undergrad I would like to make the following remark, I really really do not care about interpretations. To me teaching and studying of such questions should probably be best done in the philosophy department.

I can’t say one interpretation is better than another because they do not lead a better theory with more predictive power. Also, can interpretations be falsified by experimental results?

I would like to know what others think about the importance of having a good interpretation.

Mark, I think there might be a need here to distinguish between “interpretations” and “foundations” when speaking of QM. While it is perhaps debatable that specific interpretations have lead to new physics, it is quite clear that foundational studies have (most notably the field of quantum information). Since it seems difficult (though not necessarily impossible) to separate the study of interpretations from the study of foundations I would argue it is, in some sense, a necessity if one is interested in discovering truly new physics. One could always forego this and simply continually reapply the usual equations in a variety of ways to see what pops out, but, to me, foundational work is at the heart of all science. Foundational studies are at the heart of true innovation in science, in my honest opinion. In fact, having been an engineer for a number of years, I have had the growing feeling that physics is looking more and more like engineering. Now, don’t get me wrong, there is some truly fantastic innovation in engineering as well and even utilitarianism has its place, but making those conceptual leaps (or paradigm shifts if you subscribe to the Kuhnian view) requires studying the foundations of something. In QM I would argue that this, in essence, partly entails studying interpretations.

[Note to Matt: wish this blog software had a preview option.] To clarify, I do not think it is necessary to separate foundations from interpretations to discover new physics. That sentence should have really been two sentences and implied that foundational work is required to discover new physics, whether or not you attempt to separate out the study of interpretations (which would be difficult). Hopefully that clears up that statement (which gives a false impression upon first reading it).

Looking back at all the QM courses I took including those in my undergrad I would like to make the following remark, I really really do not care about interpretations.

Really? Then why are you reading a blog about the foundations of quantum theory? Seriously though, no one can be expected to care about everything they learn in their undergraduate courses, but that doesn’t mean that they shouldn’t be taught it. From my point of view, I can say that solving endless variations on the atomic model with ever more sophisticated interactions included via perturbation theory was not my idea of a fun party, but it was good for me to learn it nonetheless.

My view on foundations is that it will be useful for physicists to have at least a little more understanding than is the norm at present, because these issues become important when applying quantum theory in new regimes. For example, the arguments that raged over the quantum Zeno effect for several years could have been avoided if physicists had a more sophisticated understanding of the meaning and limited applicability of the projection postulate. That’s just one example, but there are many others involving things like entanglement, naive reasoning about the “path” that a particle takes in an interferometer, macroscopic superpositions, etc. As experiments become more sophisticated these things become more relevant and foundational studies are the right way to understand them. Interpretations are a relevant component of this because they can often help to understand the errors in naive intuitions.

I can’t say one interpretation is better than another because they do not lead a better theory with more predictive power. Also, can interpretations be falsified by experimental results?

Even if they don’t they may lead to a new understanding of how to apply the theory domains where it is unclear how to proceed – quantum gravity being one of the main candidates. Newton’s laws are (roughly) equivalent to Hamiltonian and Lagrangian mechanics. Does this mean you shouldn’t have bothered learning the latter two formulations?

I would like to know what others think about the importance of having a good interpretation.

Well, again you are reading a quantum foundations blog so you’re unlikely to get an unbiased opinion here. My advice is to go and read “Speakable and Unspeakable” by John Bell to find out why he said “What could be more practical than a good interpretation?” and see if you agree with him.

[Note to Ian: Since I’m on wordpress.com and not running wordpress on my own server, I don’t have a lot of control over what features are available. However, stay tuned as big changes are afoot in the not too distant future.]